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Generalized Inv-Log-Gamma-G processes. (English) Zbl 1420.60058

Summary: Gamma processes belong to subordinators for which very small jumps occurs infinitely many times in any finite time interval but their sums are finite. Here we consider their novel and important modifications with a nice application potential. A generalization of fractional \(k\)th lower record value process defined in M. Bieniek and D. Szynal [Probab. Math. Stat. 24, No. 1, 27–46 (2004; Zbl 1071.60035)], called Inverse-Log-Gamma-G process is investigated. Explicit relation with the Gamma process is presented and conditional, posterior and finite dimensional distributions are derived. The results are obtained by appropriate transformations of known stochastic processes. In contrast with the regression this allows us to describe the finite dimensional distributions of the processes of interest and in this way to make their full characterization.

MSC:

60G70 Extreme value theory; extremal stochastic processes
60J25 Continuous-time Markov processes on general state spaces

Citations:

Zbl 1071.60035
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References:

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